// NOTE THAT THIS FILE IS BASED ON MATERIAL FROM:

// Magic Software, Inc.
// http://www.geometrictools.com/
// Copyright (c) 2000, All Rights Reserved
//
// Source code from Magic Software is supplied under the terms of a license
// agreement and may not be copied or disclosed except in accordance with the
// terms of that agreement.  The various license agreements may be found at
// the Magic Software web site.  This file is subject to the license
//
// FREE SOURCE CODE
// http://www.geometrictools.com/License/WildMagic3License.pdf

#ifndef __Quaternion_H__
#define __Quaternion_H__

#include "mathbase.h"
#include "Vector3.h"
#include "Matrix3.h"

namespace PBVP {
	/** 
	 * Implementation of a Quaternion, i.e. a rotation around an axis.
	 * 
	 */
	class Quaternion
	{
	public:
		inline Quaternion (
			Real fW = 1.0,
			Real fX = 0.0, Real fY = 0.0, Real fZ = 0.0)
		{
			w = fW;
			x = fX;
			y = fY;
			z = fZ;
		}
		/// Construct a quaternion from a rotation matrix
		inline Quaternion(const Matrix3& rot)
		{
			this->FromRotationMatrix(rot);
		}
		/// Construct a quaternion from an angle/axis
		inline Quaternion(const Radian& rfAngle, const Vector3& rkAxis)
		{
			this->FromAngleAxis(rfAngle, rkAxis);
		}

		/// Construct a quaternion from 3 orthonormal local axes
		inline Quaternion(const Vector3& xaxis, const Vector3& yaxis, const Vector3& zaxis)
		{
			this->FromAxes(xaxis, yaxis, zaxis);
		}
		/// Construct a quaternion from 3 orthonormal local axes
		inline Quaternion(const Vector3* akAxis)
		{
			this->FromAxes(akAxis);
		}
		/// Construct a quaternion from 4 manual w/x/y/z values
		inline Quaternion(Real* valptr)
		{
			memcpy(&w, valptr, sizeof(Real)*4);
		}

		/// Array accessor operator
		inline Real operator [] ( const size_t i ) const
		{
			assert( i < 4 );

			return *(&w+i);
		}

		/// Array accessor operator
		inline Real& operator [] ( const size_t i )
		{
			assert( i < 4 );

			return *(&w+i);
		}

		/// Pointer accessor for direct copying
		inline Real* ptr()
		{
			return &w;
		}

		/// Pointer accessor for direct copying
		inline const Real* ptr() const
		{
			return &w;
		}

		void FromRotationMatrix (const Matrix3& kRot);
		void ToRotationMatrix (Matrix3& kRot) const;
		void FromAngleAxis (const Radian& rfAngle, const Vector3& rkAxis);
		void ToAngleAxis (Radian& rfAngle, Vector3& rkAxis) const;
		
		void FromAxes (const Vector3* akAxis);
		void FromAxes (const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis);
		void ToAxes (Vector3* akAxis) const;
		void ToAxes (Vector3& xAxis, Vector3& yAxis, Vector3& zAxis) const;
		/// Get the local x-axis
		Vector3 xAxis(void) const;
		/// Get the local y-axis
		Vector3 yAxis(void) const;
		/// Get the local z-axis
		Vector3 zAxis(void) const;

		inline Quaternion& operator= (const Quaternion& rkQ)
		{
			w = rkQ.w;
			x = rkQ.x;
			y = rkQ.y;
			z = rkQ.z;
			return *this;
		}
		Quaternion operator+ (const Quaternion& rkQ) const;
		Quaternion operator- (const Quaternion& rkQ) const;
		Quaternion operator* (const Quaternion& rkQ) const;
		Quaternion operator* (Real fScalar) const;
		friend Quaternion operator* (Real fScalar,const Quaternion& rkQ);

		Quaternion operator- () const;
		inline bool operator== (const Quaternion& rhs) const
		{
			return (rhs.x == x) && (rhs.y == y) &&
				(rhs.z == z) && (rhs.w == w);
		}
		inline bool operator!= (const Quaternion& rhs) const
		{
			return !operator==(rhs);
		}
		// functions of a quaternion
		Real Dot (const Quaternion& rkQ) const;  // dot product
		Real Norm () const;  // squared-length
		/// Normalises this quaternion, and returns the previous length
		Real normalise(void); 
		Quaternion Inverse () const;  // apply to non-zero quaternion
		Quaternion UnitInverse () const;  // apply to unit-length quaternion
		Quaternion Exp () const;
		Quaternion Log () const;

		// rotation of a vector by a quaternion
		Vector3 operator* (const Vector3& rkVector) const;

		/** Calculate the local roll element of this quaternion.
		@param reprojectAxis By default the method returns the 'intuitive' result
		that is, if you projected the local Y of the quaternion onto the X and
		Y axes, the angle between them is returned. If set to false though, the
		result is the actual yaw that will be used to implement the quaternion,
		which is the shortest possible path to get to the same orientation and 
		may involve less axial rotation. 
		*/
		Radian getRoll(bool reprojectAxis = true) const;
		/** Calculate the local pitch element of this quaternion
		@param reprojectAxis By default the method returns the 'intuitive' result
		that is, if you projected the local Z of the quaternion onto the X and
		Y axes, the angle between them is returned. If set to true though, the
		result is the actual yaw that will be used to implement the quaternion,
		which is the shortest possible path to get to the same orientation and 
		may involve less axial rotation. 
		*/
		Radian getPitch(bool reprojectAxis = true) const;
		/** Calculate the local yaw element of this quaternion
		@param reprojectAxis By default the method returns the 'intuitive' result
		that is, if you projected the local Z of the quaternion onto the X and
		Z axes, the angle between them is returned. If set to true though, the
		result is the actual yaw that will be used to implement the quaternion,
		which is the shortest possible path to get to the same orientation and 
		may involve less axial rotation. 
		*/
		Radian getYaw(bool reprojectAxis = true) const;		
		/// Equality with tolerance (tolerance is max angle difference)
		bool equals(const Quaternion& rhs, const Radian& tolerance) const;

		// spherical linear interpolation
		static Quaternion Slerp (Real fT, const Quaternion& rkP,
			const Quaternion& rkQ, bool shortestPath = false);

		static Quaternion SlerpExtraSpins (Real fT,
			const Quaternion& rkP, const Quaternion& rkQ,
			int iExtraSpins);

		// setup for spherical quadratic interpolation
		static void Intermediate (const Quaternion& rkQ0,
			const Quaternion& rkQ1, const Quaternion& rkQ2,
			Quaternion& rka, Quaternion& rkB);

		// spherical quadratic interpolation
		static Quaternion Squad (Real fT, const Quaternion& rkP,
			const Quaternion& rkA, const Quaternion& rkB,
			const Quaternion& rkQ, bool shortestPath = false);

		// normalised linear interpolation - faster but less accurate (non-constant rotation velocity)
		static Quaternion nlerp(Real fT, const Quaternion& rkP, 
			const Quaternion& rkQ, bool shortestPath = false);

		// cutoff for sine near zero
		static const Real ms_fEpsilon;

		// special values
		static const Quaternion ZERO;
		static const Quaternion IDENTITY;

		Real w, x, y, z;

		/** Function for writing to a stream. Outputs "Quaternion(w, x, y, z)" with w,x,y,z
		being the member values of the quaternion.
		*/
		inline friend std::ostream& operator <<
			( std::ostream& o, const Quaternion& q )
		{
			o << "Quaternion(" << q.w << ", " << q.x << ", " << q.y << ", " << q.z << ")";
			return o;
		}

	};

}

#endif